Scott scored the Lions' first seven points as Columbia (9-11, 2-3 Ivy League) jumped to a 7-2 lead and never trailed.
Penn (7-13, 2-1) played without leading scorer Tyler Bernardini, who reportedly sustained a concussion in practice earlier in the week and did not accompany the team to New York.
Brian Grandieri led the Quakers with 13 points.
Columbia built a 38-23 lead with 2:51 remaining in the first half primarily because of good 3-point shooting. Eleven of the Lions' first 16 shots were 3-point attempts, and they made six.
Trailing 38-29 at halftime, the Quakers closed within seven points with 12:13 left in the second half. But Scott started a 9-0 run with a layup and Matsui's 3-pointer made it 59-43 with 8:31 to play.
Penn has lost four of its last six while the Lions have won two of three.